The traditional force cup plunger is a rubber force cup on the end of a wooden handle with a disc behind it. As the name suggests this plunger is used for forcing water down the drain, into the blockage and dislodging it. For maximum effect, with a tight seal and no air in the cup, a back and forth motion will create high and low pressure at the point of the blockage. This dual action may be needed several times to break up and release stubborn blockages from the sides of the drain.
The Cooper Plunger is part of this range and is specifically for unblocking toilets. The long T-handle gives a good grip, and the flat rubber disc ensures a tight seal. Usually a series of short sharp pushes will release the blockage.